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ECE360
HOMEWORK #4
DUE: FRIDAY, OCTOBER 5, 2007
Problem 4.1
Consider the following matrices:
A
=
1 1 0
1 0 1
0 1 1
, A
1
=
4 1 0
7 0 1
9 1 1
, A
2
=
1 4 0
1 7 1
0 9 1
, A
3
=
1 1 4
1 0 7
0 1 9
(a) Compute det(
A
), det(
A
1
), det(
A
2
), and det(
A
3
) using Sarrus’ rule for determinants.
(b) Compute det(
A
), det(
A
1
), det(
A
2
), and det(
A
3
) using Chio’s pivotal condensation method.
(c) Find
A
T
and
A

1
=
adj(
A
)
det(
A
)
Problem 4.2
Refer to Problem 4.1.
(a) Check by direct substitution that
x
1
= 1,
x
2
= 3, and
x
3
= 6 are solutions of the following
system of equations:
x
1
+
x
2
= 4
x
1
+
x
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Unformatted text preview: 3 = 7 x 2 + x 3 = 9 (b) Write this system in matrix form A x = b and solve for x = A1 b . (c) Solve for x 1 , x 2 , and x 3 using Cramer’s rule, that is, evaluate: x 1 = det( A 1 ) det( A ) , x 2 = det( A 2 ) det( A ) , x 3 = det( A 3 ) det( A ) Problem 4.3 Find e At = L1 ' ( sIA )1 “ given A = "1 11 # Problem 4.4 Refer to Problem 4.3. Find: (a) A1 (b) de At dt , Ae At , e At A (Conclude.) (c) Z t e Aτ dτ, A1 ‡ e AtI · , ‡ e AtI · A1 (Conclude.)...
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